Path planning methodologies, or trajectory planning methodologies, for example using Mixed Integer Linear Programming (MILP), are used to determine globally optimal trajectories for vehicles. Many path planning methodologies constrain vehicle trajectories with a linear approximation of the vehicle's dynamics.
Many vehicles (including, for example, cars, trucks, tracked vehicles, aircraft and boats) are subject to a minimum turning radius constraint. Such constraints tend to be difficult to include in a linear path planning problem, as such constraints are inherently nonlinear.
Many MILP processes implement additional constraints on the vehicle dynamics in order to produces a valid trajectory. However, such approaches tend to fail if an optimal solution contains velocities close to zero.